1. Tracer Particles and Seeding for PIV

2. Seeding particles for PIV
Proper tracer must be small enough to follow (trace) fluid motion and should not alter fluid or flow properties.
Proper tracer must be large enough to be visible by the camera.
Uniform seeding is critical to the success of obtaining velocity field. No seed particles, no data.
The seeding source must be placed cleverly so that the particles mix with the flow well.
Particles with finite inertia are known to disperse non-uniformly in a turbulent flow, preferential concentration
PIV relies highly on scattering particles suspended in the flow to provide the velocity information for the continuous medium (liquid or gas).
The accuracy of the velocity field determination is ultimately limited by the ability of the scattering particles to follow the instantaneous motion of the continuous phase.
A compromise between reducing the particle size to improve flow tracking and increasing the particle size to improve light scattering is, therefore, necessary.
Proper flow seeding is particularly critical with PIV.

3. Seeding particles for PIV (cont’d)
The tracing ability and the dispersion characteristics depends on the aerodynamical characteristics of particles and the continuous medium;
The visibility depends on the scattering characteristics of particles.
The choice of optimal diameter for seeding particles is a compromise between two aspects.
The choice of optimal diameter for seeding particles is a compromise between a quick response of the tracer particles in the fluid, requiring small diameters, and a high signal-to-noise ratio (SNR) of the particle images, necessitating large diameters.

4. Scattering characteristics of particles
Laser sheet leads to a low energy density – particle scattering efficiency is important;
Light scattering capability - scattering cross section Cs is defined as the ratio of the total scattered power Ps, to the laser intensity I0 incident on the particle
Even when using high laser pulse energies, the distribution of this energy over a laser sheet leads to an energy density that is low relative to other laser diagnostic instruments, say LDV. Hence, particle scattering efficiency is very important for PIV particles.
A convenient measure of the (spatially integrated) light scattering capability is the scattering cross section Cs, defined as the ratio of the total scattered power Ps, to the laser intensity I0 incident on the particle: Cs = Ps / I0. Figure 1 shows the variation of Cs as a function of the ratio of the particle diameter dp to the laser wavelength  for spherical particles with a refractive index m = 1.6. Table 1 compares approximate values for a diatomic molecule such as nitrogen or oxygen and two larger particles.

5. Example of scattering cross section (1)
These examples indicate clearly the enormous difference between the light scattering cross sections of molecules and those of particles that are typical seeds for PIV experiments. Elastic (Rayleigh) scattering from molecules is far too weak for PIV even with illumination by a laser of maximum available power or pulse energy. In terms of SNR, PIV applications are confronted with lower incident light intensity compared with LDV, consequent on spreading the laser energy spatially over a light sheet.
The scattering cross section as a function of the particle size (refractive index m=1.6).

6. Example of scattering cross section (2)
Diameter dp
Scattering cross section Cs
Molecule
10-33m2
1m
Cs(dp/)4
10-12m2
10m
Cs( dp/)2
10-9m2
Scattering cross section as a function of the particle size

7. Mie scattering of small particle (1)
In PIV experiments one normally observes light scattered at 90o from the incident light sheet. Studies of scattering from spherical particles have shown that the intensity ratio Is90/Is0 of 90o scattered light to forward scattered light is a strong function both of the size parameter dp/ and of the refractive index m. The angular distribution of scattered light in the vicinity of 90o is complex, with several nodes whose exact positions are strongly size dependent.
Light Scattering by an oil particle in air when refractive index m ~ 1.4. Left: 1mm diameter, right: 10mm diameter

8. Mie scattering of small particle (2)
Light scattering by a 1 mm, 10 mm, and 30 mm glass particle in water. Refractive index m = 1.52

9. Summary of particle light scattering for PIV
The ratio Is90/Is0 decreases with increasing size parameter dp/, with values roughly in the range for scattering particles useful in PIV.
The resulting intensity of the scattered light for a given light sheet intensity will depend on the combined influences of Cs and Is90/Is0, which exhibit opposing tendencies with increasing particle size. In general, larger particles will still give stronger signals.
The ratio Is90/Is0 increases with increasing refractive index m. Hence particles in air gives stronger 90o scattering than in water.

10. Tracking characteristics of particles
The tracking ability depends on
Particle shape – assumed spherical – aerodynamically equivalent diameter - dp
Particle density p
Fluid density f and fluid dynamic viscosity  or kinematic viscosity = /f
Newton’s Law governing the motion of a single particle:
{sigma_f} where includes all forces experienced by the particle.

11. General governing equation
Meaning of each term:
Viscous drag according to the Stokes’ law
Acceleration force
Force due to a pressure gradient in the vicinity of the particle
Resistance of an inviscid fluid to the acceleration of the sphere (“added mass”)
Basset history integral – resistance caused by the unsteadiness of the flow field.

12. Stokes’ drag law
The Stokes’ drag law is considered to apply when the particle Reynolds number Rep is smaller than unity, where Rep is defined as
In a typical PIV experiment with 10m particles and 20 cm/s mean velocity, Rep=10x10-6 x 0.2 / 1.46x10-5 = 0.13 (air); Rep=10x10-6 x 0.2/1.0x10-6 = 2 (water).
Apparently, the case of water deviates from the linear Stokes drag, but most simulations still assume Stokes linear drag. Stokes’ drag low gives a conservative estimate of the tracking ability of particle, since the actual drag tends to be higher.

13. Particle parameter - the particle response time tp
Velocity lag of a particle in a continuously accelerating fluid:
The particle velocity response to the fluid velocity if heavy particles (p>>f) in a continuously accelerating flow is:
Particle response time:
In the most cases of PIV measurements, many terms appeared in the equation can be neglected expect the term of Stokes’ drag since usually the particle Reynolds number Rep appeared in these cases is on the order of unity. If there is no external force exerted on particle, the velocity lag (difference between velocities of particle and fluid where the particle occupies) of a particle in a continuously accelerating fluid can be expressed:
p is a convenient measure of the tendency of particles to follow the flow, even if the acceleration of the fluid is not constant or if the Stokes drag law does not apply.
p is the particle response time. It is a measure of the particle inertia.

14. Particle parameter - the Stokes number St
Stokes number St as the ratio of the particle response time to the Kolmogorov time scale:
St: the degree of coupling between the particle phase and the fluid.
St0 the particles behave like tracers
St the particles are completely unresponsive to the fluid flow.
The particle response time should be evaluated against the turbulence time scale, i.e., the turn-over time of the relevant turbulent structure. In a fully developed turbulent flow, we often use the Kolmogorov time scale, denoted k, which is the turn-over time of the smallest eddy.
For this purpose, we de fine Stokes number St as the ratio of the particle response time to the Kolmogorov time scale:
St determines the degree of coupling between the particle phase and the fluid. At St0 the particles behave like tracers while St the particles are completely unresponsive to the fluid flow.

15. Particle parameter - the characteristic frequency C
In the case of gas flow where p>>f, characteristic frequency of the particle motion
Tracing ability in turbulence, c=2fc
In the case of gas flow where p>>f, the response of particle to turbulence frequency needs to be considered. If c=2fc is the highest turbulence frequency of interest, C is a characteristic frequency of the particle motion, the following equation can be used to determine the tracing ability.

16. Figure of characteristic frequency
Figure ?? shows the ratio of fluctuation intensities of the particle and fluid motion in a turbulence flow summed over all turbulence frequencies below fc. The curve for C=1.2x105s-1 corresponds approximately to the motion of a 1m water droplet in air. Higher C values lead to better flow tracking behavior of the particle.
The response of particles in turbulence flow. (From Haetig J, Introductory on particle behavior ISL/AGRAD workshop on laser anemometry (Institute Saint Louis) report R 117/76, 1976)

17. Particle size vs. Turbulence scale
Seeding particles need to be smaller than the smallest turbulence scale if one wants to identify all the structures in the vicinity of the flow. The smallest fluid length scale is called the Kolmogorov length scale, and it is related to the size of the smallest eddy.

18. Additional Considerations
Particle seeding uniformity
St <<1 St ~ 1 St >>1
Hence, it is important, for data uniformity point of view, to choose small Stokes number tracer particles.

19. Additional Considerations (cont’d)
Secure sufficient spatial detail in the flow field a higher concentration of particles is generally needed with PIV than with LDV, with which it is possible to wait indefinitely for the arrival of a scattering particle in the probe volume.
A uniform particle size is desirable in order to avoid excessive intensity from larger particles and background noise, decreasing the accuracy, from small particles.
Particles that naturally exist in the flow seldom meet the above requirements. Hence, in PIV applications, it is often necessary to seed the flow with a chosen tracer particle. The particles are either premixed with the whole fluid (e.g., stirred ) or released in situ by a seeding source.
Furthermore, to secure sufficient spatial detail in the flow field a higher concentration of particles is generally needed with PIV than with LDV, with which it is possible (within limitations imposed by flow unsteadiness, biased sampling of the velocity statistics or running costs) to wait indefinitely for the arrival of a scattering particle in the probe volume.
A uniform particle size is desirable in order to avoid excessive intensity from larger particles and background noise, decreasing the accuracy, from small particles. A uniform seeding is also important for correlation calculation, where large particles would produce a bias of correlation result towards large tracers, therefore compromising the measurement accuracy.
Particles that naturally exist in the flow (such as impurity in water) seldom meet the above requirements. Hence, in PIV applications, it is often necessary to seed the flow with a chosen tracer particle. The particles are either premixed with the whole fluid (e.g., stirred ) or released in situ by a seeding source.

20. Imaging of small particles
Relation between real particles and particle image recorded in the camera can be analyzed by the diffraction limited imaging of a small particle
For a given aperture
diameter Da and wavelength , the Airy spot size
If plane light waves impinge on an opaque screen containing a circular aperture they generate a far-field diffraction pattern on a distant observing screen. By using a lens, e.g. an objective in a camera, the far field pattern can be imaged on an image sensor close to the aperture without changes. However, the image of a distant point source (e.g. a small scattering particle inside the light sheet), does not appear as a point in the image plane but forms a Fraunhofer diffraction pattern even if it is imaged by a perfectly aberration-free lens. A circular pattern, which is known as the Airy disk, will be obtained for a low exposure. Surrounding Airy rings can be observed for a very high exposure.
Using an approximation (the so-called Fraunhofer approximation) for the far field it can be shown that the intensity of the Airy pattern represents the Fourier transform of the aperture's transmissivity distribution. Considering the scaling theorem of the Fourier transform large aperture diameters correspond to small Airy disks and small apertures to large disks.

21. Imaging of small particles (cont’s)
With an imaging lens, the diffraction-limited size:
Estimate of the particle image diameter:
The Airy function can mathematically be represented by the square of the first order Bessel function. Therefore, the first dark ring, which defines the extension of the Airy disk, corresponds to the first zero of the first order Bessel function. The Airy function represents the impulse response, the point spread function, of an aberration-free lens. We will now determine the diameter of the Airy disk ddiff, because it represents the smallest particle image that can be obtained for a given imaging configuration.
The magnification factor M=z0/Z0, f# is the f-number defined as the ratio between the focal length f and the aperture diameter Da, the image of a finite-diameter particle is given by the convolution of the point spread function with the geometric image of the particle. If lens aberrations can be neglected and the point spread function can be approximated by the Airy function, the following formula can be used for an estimate of the particle image diameter:
dp: original particle diameter

22. Seeding particles for PIV (liquid flow)
For most experiments it is desirable that seeding particles be non-toxic, non-corrosive, non-abrasive, non-volatile and chemically inert. Considering these requirements, a wide variety of seeding particles is available for PIV experiments. Tables 1 and 2 are the general guidance of selecting proper particles for PIV.

23. Seeding particles for PIV (gas)
For most experiments it is desirable that seeding particles be non-toxic, non-corrosive, non-abrasive, non-volatile and chemically inert. Considering these requirements, a wide variety of seeding particles is available for PIV experiments. Tables 1 and 2 are the general guidance of selecting proper particles for PIV.

24. Commercial seeding particles - TSI (http://www.tsi.com)
Silicon Carbide: Suitable for measurements in liquids and gases, silicon carbide particles have a narrow particle size distribution (mean diameter of 1.5m). Their high refractive index is useful for obtaining good signals in water, even in backscatter operation. They can also be used in high temperature flows. Supplied as a dry powder, they can be mixed in liquid to form a suspension before dispersing.
Titanium Dioxide: Titanium dioxide particles (mean diameter of 0.2m) are usually dispersed as a dry powder for gas flow measurement applications. The smaller particle size makes titanium dioxide attractive for high-speed flows. It can also be used for high temperature flows.

25. Commercial seeding particles - TSI (http://www.tsi.com) (cont’d)
Polystyrene Latex: With an extremely narrow size distribution (nominal diameter of 1.0m), polystyrene latex (PSL) particles are useful in many different measurements. Supplied in water, they are not recommended for high temperature applications.
Metallic coated: Metallic coated particles (mean diameter of 9.0m) are normally used to seed water flows for LDV measurements due to their lower density and higher reflectivity. They cannot be used where salt is present. Salt reacts with the metal coating, causing the particles to agglomerate and drop out of the flow.

26. Commercial seeding particles - TSI (http://www.tsi.com) (cont’d)

27. Commercial seeding particles - Dantec (http://www.dantecmt.com)
Polyamide seeding particles (PSP): These are produced by polymerisation processes and therefore have a round but not exactly spherical shape. They are microporous and strongly recommended for water flow applications.
Hollow glass spheres and silver-coated hollow glass spheres (HGS, S- HGS): Intended primarily for liquid flow applications, these are borosilicate glass particles with a spherical shape and a smooth surface. A thin silver coating further increases reflectivity.
Fluorescent polymer particles (FPP): These particles are based on melamine resin. Fluorescent dye (Rhodamine B:) is homogeneously distributed over the entire particle volume. In applications with a high background light level, fluorescent seeding particles can significantly improve the quality of vector maps from PIV and LDV measurements. The receiving optics must be equipped with a filter cantered on the emission wavelength (excitation max.: 550 nm; emission max.: 590 nm).

28. Commercial seeding particles - Dantec (http://www. dantecmt
Commercial seeding particles - Dantec ( (cont’d)

29. Particle generation Liquid flow Gas flow Requirement for PIV
Simple, select proper powder then mix w/ liquid
Gas flow
liquid droplets
Atomization or Condensation
solid particles
Atomization or Fluidization
Requirement for PIV
Nearly monodisperse size distribution
High production rate
Particle generation and supply
Descriptions of seeding particles and their characteristic s have been given in many scientific publications. In contrast to that, little information can be found in the literature on how to practically supply the particles into the flow under investigation. Sometimes seeding can be done very easily or does not even have to be done. The use of natural seeding is sometimes acceptable, if enough visible particles are naturally present to act as markers for PIV.
In almost all other work it is desirable to add tracers in order to achieve sufficient image contrast and to control particle size. For most liquid flows this can easily be done by suspending solid particles into the fluid and mixing them in order to get a homogeneous distribution. In gas flows the supply of tracers is very often more critical for the quality and feasibility of the PIV measurement and the health of the experimentalists. The particles which are often used are not easy to handle because: 1) many liquid droplets tend to evaporate rather quickly and; 2) solid particles are difficult to disperse and very often agglomerate. The particles can therefore not simply be supplied for a long time before the measurement, but must be in­jected into the flow shortly before the gaseous medium enters the test section. Furthermore, the injection has to be done without significantly disturbing the flow, but in a way and at a location that ensures homogeneous distribution of the tracers.
A number of techniques are used to generate and supply particles for seeding gas flows: dry powders can be dispersed in fluidized beds or by air jets. Liquids can be evaporated and afterward condensed in conden­sation generators, or liquid droplets can directly be generated in atomizers. Atomizers can also be used to disperse solid particles suspended in evap­orating liquids, or to generate tiny droplets of high vapor pressure liquids (e.g. oil) that have been mixed with low vapor pressure liquids (e.g. alcohol) which evaporate before the test section. For seeding wind tunnel flows condensation generators, smoke generators and monodisperse polystyrene or latex particles injected with water‑ethanol are most often used for flow visu­alization and LDV. For most of the PIV measurements in air flows Laskin nozzle generators and oil have been used. These particles offer the advantage of not being toxic; they stay in air at rest for hours, and do not change in size significantly under various conditions. In recirculating wind tunnels they can be used for a global seeding of the complete tunnel volume or for a local seeding of a stream tube by a seeding rake with a few hundred tiny holes.
The design of the seeding device is highly dependent on the experiment to be conducted.

30. Liquid droplets Advantage Problem Generator Steady production rate;
Inherently spherical shape;
Known refractive index
Problem
Form non‑uniform liquid films on window
Generator
Laskin atomizer
Commercial atomizer (e.g., TSI)
Generally solid particle is from powder. In practical,
Seeding with liquid droplets offers the advantage of a steadier production rate than is normally feasible with solid particles. Their inherently spherical shape is also advantageous for assessing tracking behaviour and scattering characteristics; moreover, information on the refractive index is more readily available for liquids than it is for many solids. Seeding droplets depositing on windows in internal flows can form non‑uniform liquid films, leading to beam distortion by refraction; the consequent defocusing or deflection may be serious enough to cause temporary or permanent loss of signals.